If you had not already owned a few lenses for Canon, it would be the NEX-6, hands down.
The NEX-6 has much better image quality--especially in low light--than the T3. There is no comparison.
I've done several tests with a T4, D5100, and NEX-5N and the results were quite remarkable:
When use in P mode (camera chooses shutter speed, aperture, and ISO based upon metering and scene)) using equivalent kit lenses (18-55) in low light situations, the NEX would usually focus with a shutter speed at least 30-75% faster than the T4 and 50-80% faster than the D5100
When used with full manual controls (same aperture, focal length, shutter speed, and ISO settings), the NEX shoots a MUCH brighter photo than the T4 and the D5100
Remember, the NEX-5N uses the same sensor as the Nikon D7000 (a much more expensive camera than both the T4, D5100, and NEX) and the NEX-6 has an improved sensor over the 5N (slightly better noise control, much more accurate white balance).
However, you WILL NOT get the most out of the camera with just its kit lens. All things being equal, I would take an inferior camera with better glass (lenses) over a superior camera with its kit lens any day.
Zoom lenses (especially the kit zooms that come with a camera for JUST 100 bucks or maybe a little more) have much narrower aperture ranges than, say, a higher quality zoom and especially a high quality prime (single focal distance) lens.
The wider the aperture, the more light you can let in and the more control you can have over shallow depth of field (the blurring of background objects compared to your subject).
That being said, owning just the kit lens, a macro and a fisheye does not seem all that significant for my shooting needs. I prefer shootings portraits and sports (people!).
Of course, this is all up to your own tastes. You can always buy an adapter to use Canon lenses (even new ones) with the NEX-6 (you will have to use manual focusing), but that's part of the charm of the NEX system. I have bought many old lenses in the past year with my 5N ranging from Jupiter, Leica, Nikon, and Minolta and I absolutely LOVE shooting with legacy lenses. I enjoy it even more now that I bought my NEX-6 and can use the EVF.
It's all a matter of your needs as a photographer. The size, speed, and technology difference may necessitate you giving up some lenses (or at least giving up on auto-focus), but I definitely prefer my NEX-6 over anything below a full-frame that Nikon or Canon have come up with this year.